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High-precision cosmology requires the analysis of large-scale surveys in 3Dspherical coordinates, i.e. spherical Fourier-Bessel decomposition. Currentmethods are insufficient for future data-sets from wide-field cosmologysurveys. The aim of this paper is to present a public code for fast sphericalFourier-Bessel decomposition that can be applied to cosmological data or 3Ddata in spherical coordinates in other scientific fields. We present anequivalent formulation of the spherical Fourier-Bessel decomposition thatseparates radial and tangential calculations. We propose the use of theexisting pixelisation scheme HEALPix for a rapid calculation of the tangentialmodes. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Besseldecomposition of 3D all-sky surveys that takes advantage of HEALPix for thecalculation of tangential modes. We perform tests on very large simulations andwe compare the precision and computation time of our method with an optimisedimplementation of the spherical Fourier-Bessel original formulation. Forsurveys with millions of galaxies, computation time is reduced by a factor 4-12depending on the desired scales and accuracy. The formulation is also suitablefor pre-calculations and external storage of the spherical harmonics, whichallows for additional speed improvements. The 3DEX code can accommodate datawith masked regions of missing data. 3DEX can also be used in otherdisciplines, where 3D data are to be analysed in spherical coordinates. Thecode and documentation can be downloaded at http://ixkael.com/blog/3dex.

3DEX: a code for fast spherical Fourier-Bessel decomposition of 3D surveys